Trace Dynamics as a model for emergent spacetime

7th International Conference on Gravitation and Cosmology

Lochan, K.^1 ; Singh, T.P.^1

Tata Institute of Fundamental Research, Homi Bhabha Road, Colaba, Mumbai 400005, India^1

关键词: Classical theory;    Commuting matrix;    Cyclic permutations;    Lorentz transformations;    Operator structures;    Relativistic dynamics;    Space-time coordinates;    Special relativity;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/484/1/012065/pdf
DOI  :  10.1088/1742-6596/484/1/012065

来源: IOP

【 摘 要 】

Trace Dynamics is a classical theory of non-commuting matrices, which uses cyclic permutation inside a trace to define the derivative with respect to an operator. We have used the methods of Trace Dynamics to construct a non-commutative special relativity. We have defined a line-element using the trace over spacetime coordinates, which are assumed to be operators. The line-element is shown to be invariant under generalized Lorentz transformations, and is used to construct a non-commutative relativistic dynamics. We have been motivated for such an operator structure at a more fundamental level, and attempt to obtain an emergent picture of classical spacetime.